SINFIT4

Purpose:

Fits y(x) = A cos(2πfx + B) + C by iterative least squares.

Syntax:

SINFIT4(series, freq, niter, tol)

series	-	A series, the input sinusoid
freq	-	A real, the starting frequency for the iteration process. Defaults to -1, estimate the frequency.
niter	-	Optional. An integer, the maximum number of least squares iterations if no convergence. Defaults to 30.
tol	-	Optional. A real, the relative frequency convergence tolerance. Defaults to 1e-6.

Returns:

A series, the fitted sine curve.

(fit, coef) = SINFIT4(series) returns the fit and coefficients.

(fit, coef, rmserr) = SINFIT4(series) returns the fit, coefficients and RMS error.

Example:

W1: 5 + 3 * gsin(1000, .001, 4, pi) + gnorm(1000, .001)

W2: sinfit4(w1);overp(w1, lred)

Overplots the original data with the fitted sinusoid.

Example:

(fit, coef) = sinfit4(w1)

fit is the same as W2.

coef == {2.996476, 4.009087, 1.549703, 4.999965}} or similar such that:

A == coef[1]

f == coef[2]

B == coef[3]

C == coef[4]

Example:

(fit, coef, rmserr) = sinfit4(w1, 4)

fit contains the fitted data.

coef == {3.0012, 4.0000, 1.5706, 5.000} or similar.

rmserr == 0.998756

Remarks:

SINFIT4 uses the iterative least squares method to fit a sinusoid with a starting input frequency as per the IEEE 1241 Standard such that:

$image\lsinfit02.gif$

If the input frequency is unspecified, the frequency is estimated by using SINFIT3. SINFIT3 is also used as the starting point for the iterative least squares fit. Given the specified or estimated starting frequency, the frequency is adjusted to minimize the least squares error to the tolerance value.

The frequency coefficient, F = coef[2] is in Hertz and θ, the phase term, B = coef[3] is in radians.

The starting frequency, if specified, may differ from the resulting fitted frequency. See SINFIT3 to perform a fit that preserves a known frequency. SINFIT3 is an implementation of the 3 term sinusoid fit as outlined in the IEEE 1241 Standard.

References:

IEEE Std 1241-2010 Annex B.2 "An algorithm for four-parameter least-squares fit to sine-wave data"

SINFIT4

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